Great Dodecahedron

One of the four Kepler-Poinsot solids. It consists of twelve intersecting
pentagons. It is also a stellation of the
dodecahedron, and a faceting of the
icosahedron.

To give the model internal support, I printed out three big pentagons
to fit inside, and built three of the star parts shown on the left.

The three strengthened parts fit together, with other trihedral dimples
filling in the gaps to complete the model.

Here's a topological version. In this version parts of each
face have been cut away so that only faces that truly share an edge are
still connected. Where two faces would normally intersect to cause a
false edge, now they weave through each other without collision.